Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics

Details Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics

2004-10-22

arxiv.org/abs/quant-ph/0410173v1

Physics

Quantum Physics

Scientific paper

We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear canonical transformations, the other focuses on the generating function which satisfies the Hamilton-Jacobi equation in classical mechanics. We also show that these two methods lead to the same solution of the Schr\"{o}dinger equation.

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